This page serves as a sort of journal for Geoff’s doctoral program, separate from the Emergentmath blog. Here, Geoff will share thoughts and reflections on classes, insights into literature and other PhD-related musings. While you’re here, feel free to explore Geoff’s main blog, various “miniseries,” and select blog posts. Here is Geoff’s About Me page.

Week 1

Journal: Belonging
Research Reflection: Mathematics as a(n unwilling) participant in restorative circle

Wednesday 8/26/2020

I’m a bit of a veteran when it comes to false starting a PhD program. In 2010, I had been accepted to the CU-Boulder Atmospheric Science PhD program. However, I received a job offer from New Tech Network I couldn’t turn down the week before I was supposed to start classes. Technically, I did not drop out because I never began. The job entailed traveling to schools throughout the country to support math teachers: observing, coaching, and co-designing dynamic math classrooms.

In 2014, it was more of a full on drop-out. I enrolled in the Colorado State University Education PhD program. I attended classes for aa few weeks before I withdrew from the program with little fanfare. I felt awful letting down my advisor, who would have absolutely been a great resource and professor had I stayed on. The breaking point was one particular week (mind you, I’d only had perhaps three weeks total under my belt at the time). I was dwelling on a work trip at the expense of an exam, which I ended up doing poorly on. My family was stressed out as I was ever in-between work and school. It became clear that between school, work, and family I had to pick two. I chose work and family. Had the CSU program been more suited to my predilections and values, I might have held out. But the truth is, it wasn’t what I truly desired in a program.

Rockinson-Szapkiw and Spaulding (2014) begin Navigating the Doctoral Journey with a discussion about finding the right program. Had I considered this more deeply in 2010 and 2014, I might have saved a lot of consternation and a not-negligible amount of non-refundable tuition. I overvalued the proximity of CSU and undervalued the draw of the program itself.

After three days of classes, I’m eminently confident I’ll complete the University of Wyoming Math Education program. The program itself is more attuned to my research and career aspirations. Already, we’ve discussed racial equity (or lack thereof) in Mathematics classes, alongside how to develop learner-centric math classrooms. In addition to the Math Education program, the existence of the Intro to Doctoral Studies class suggests a level of support for PhD students that will meet my needs.

Too, having been unceremoniously let go from my aforementioned job at New Tech Network, there’s a greater impetus (and time allowance) for me to finally achieve the goal I’ve always wanted: to be a part of the conversation in the next generation of math instruction. Between these external factors and my internal renewed desire to make math more accessible, I’m greatly anticipating every moment of this program.

After all, the third time’s a charm.

Rockinson-Szapkiw, A. J., & Spaulding, L. S. (2014). Navigating the Doctoral Journey: A Handbook of Strategies for Success. Rowman & Littlefield Publishers.

Friday 8/28/2020
Research Reflection: Mathematics as a(n unwilling) participant in restorative circle

Hand and Spencer (2015) lays bare the violence imparted upon children of color by mathematics instruction historically through present-day. The authors argue racism is best understood as the “accumulated advantages” offered to white students. This includes generational access to education, stability in parental employment and wealth accumulation, and countless other advantages. Students of color most not only cope with the accumulated “educational debt,” they must also actively work to counteract negative biases against them. This emotional labor only adds to the debt. Western culture and identity is the default (and therefore, most accepted) way of being. 

The following are some examples of how a racialized education system reveals itself: 

  • Students of color are less well represented in gifted programs, and are often overlooked for testing that would place them in such programs
  • Students of color are overrepresented in remedial programs, which in turn typically offer more rote tasks
  • Black students are over disciplined and are suspended at much higher rates than their white peers

Throughout the reading I was continually reminded about one of the core features of american society: it’s individualism. In Zaretta Hammond’s Culturally Responsive Teaching and the Brain (2014), we find that the U.S. ranks far and away the most individualistic society (on a spectrum that puts the U.S. at contrast with communal societies). While many see the U.S.’s commitment to individualism as a benefit, in education we see how attitudes of “what’s best for my child is of utmost importance” result in widening gaps in access to quality education. Students with upper middle class parents – and associatively well-educated parents – advocate and fight for their children to be placed in accelerated programs. What is intended to be a system of differentiation – ostensibly to differentiate based on the needs of the student – serves to reinforce longstanding hierarchies. 

The restorative justice framing of Gholson and Robinson (2019) was fascinating. In restorative practice, parties are to discuss the harm done and potential reparations for the harm. In this case, as the authors intone, “math” is one of the parties. Given that approach, it stands to reason that students need to voice the harm done and what can be done to repair their relationship with mathematics. 

The Silhouette activity presented in Gholson and Robinson (2019) remind me of some of the responses I received in a Math Attitudes Survey, particularly the emphasis on belonging (or lack thereof). I’m still taken aback when I hear that students have been told explicitly that they don’t belong in the math classroom. I expect instances of implicit bias; it’s still jarring to know so many students receive the negative end of explicit bias. The following is a selection of what some students voiced in the Silhouette activity (Table 2).

  • You won’t ever be anything
  • You’re born in ‘04?!?
  • You make me feel dumb
  • Math is not your strong suit
  • Stop raising your hand, you’re always wrong every time. 

Next week I’ll be reading the first two chapters of Dr. Janquelene Leonard’s ciCulturally specific pedagogy in the mathematics classroom. This book will help lay a path for a continued corrective to some of the challenges we see laid out in Spencer and Hand (2015) and Ghoulson and Robinson (2019).


Hammond, Z. (2014). Culturally Responsive Teaching and The Brain: Promoting Authentic Engagement and Rigor Among Culturally and Linguistically Diverse Students. SAGE Publications. 

 Leonard, J. (2019). Culturally specific pedagogy in the mathematics classroom: Strategies for teachers and students (2nd Ed.) New York: Routledge.

Maisie L. Gholson & Darrius D. Robinson (2019) Restoring MathematicsIdentities of Black Learners: A Curricular Approach, Theory Into Practice, 58:4, 347-358, DOI:10.1080/00405841.2019.1626620

Spencer, J. & Hand, V. (2015). The racialization of mathematics education. In L. Drakeford (Ed.)The Race Controversy in American Education(p.237-258). Santa Barbara, CA: Praeger.

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